Sequences

Number of meanders in which first bridge is 3.

Number of meanders in which first bridge is 5.

Number of meanders in which first bridge is 7.

Number of projective meanders.

Number of irreducible systems of meanders.

G.f.: { ( Product_{j=1..infinity} (1-x^j) - 1 )/x }^24.

Number of halving steps to reach 1 in '3x+1' problem, or -1 if this never happens.

Number of tripling steps to reach 1 from n in '3x+1' problem, or -1 if 1 is never reached.

Exponential self-convolution of Pell numbers (divided by 2).

Exponentiation of g.f. for Pell numbers.

Edge-distinguishing chromatic number of path with n nodes.

Edge-distinguishing chromatic number of cycle with n nodes.

a(n) = smallest m such that for every red-blue edge-coloring of the graph K_{m} there exists either a red 4-cycle or a blue K_{1,n}; Ramsey number r(C_4, K_{1,n}).

E.g.f. is the logarithmic derivative of e.g.f. for Pell numbers [1, 0, 1, 2, 5, ...].

Triangulations of a square with no separating triangles (previously "Bordered triangulations of sphere with n nodes").

Number of paths through an array.

Number of paths through an array.

Number of planted binary phylogenetic trees with n labels.

Number of planted binary phylogenetic trees with n labels.

Number of planted binary phylogenetic trees with n labels.

Number of binary phylogenetic trees with n labels.

Number of binary phylogenetic trees with n labels.

Number of binary phylogenetic trees with n labels.

Number of regions in certain maps.

Convolve Fibonacci and Pell numbers.

Coefficients for numerical integration.

Octavan primes: primes of the form p = x^8 + y^8.

Duodecimal primes: p = (x^12 + y^12 )/(x^4 + y^4 ).

Number of self-dual equivalence classes switching functions of exactly n+1 variables.

Number of deterministic, completely-defined, initially-connected finite automata with 2 inputs and n unlabeled states.

Number of deterministic, completely-defined, initially-connected finite automata with 3 inputs and n unlabeled states.

Normalized number of connected (n+1)-state finite automata with 2 inputs.

Number of connected n-state finite automata with 3 inputs.

Modified Engel expansion of 3/7.

Number of cyclotomic cosets of 2 mod 2n+1.

a(2n)=2*a(2n-2)^2-1, a(2n+1)=2*a(2n)-1, a(0)=2.

a(n) = min_{k=1..n} (a(k-1) + 2^k*(n + a(n-k))); a(0) = 0.

Number of subwords of length n in infinite word generated by a -> aab, b -> b.

T(2,2n), where T(k,m) is the number of sequences a_1,...,a_m of integers 0,1,...,n with n=floor(m/k) such that the 'bumped' sequence b_1,...,b_m has exactly k of each of 0,...,n-1, where b_i=a_i + j (mod n+1) with minimal j>=0 such that b_0,...,b_i contain at most k elements equal to b_i.

T(3,3n), where T(k,m) is the number of sequences a_1,...,a_m of integers 0,1,...,n with n=floor(m/k) such that the 'bumped' sequence b_1,...,b_m has exactly k of each of 0,...,n-1, where b_i=a_i + j (mod n+1) with minimal j>=0 such that b_0,...,b_i contain at most k elements equal to b_i.

T(n,3,1), where T(n,k,s) with 0<=s<n is the number of sequences a_1,...,a_(k*n+s) of integers 0,1,...,n such that the 'bumped' sequence b_1,...,b_(k*n+s) has exactly s n's, where b_i=a_i + j (mod n+1) with minimal j>=0 such that b_0,...,b_i contain at most k elements equal to b_i.

Exponentiation of g.f. for Fibonacci numbers.

Solution to a Pellian equation: least x such that x^2 - n*y^2 = +- 1.

Solution to Pellian: y such that x^2 - n*y^2 = +-1.

Solution to Pellian: x such that x^2 - n y^2 = +- 1, +- 4.

Solution to Pellian: y such that x^2 - n y^2 = +- 1, +- 4.

Self-convolution of numbers of trees on n nodes.

Expansion of a modular function.

Expansion of a modular function for gamma_0(6).

Expansion of a modular function.